A review of the author's work on the development and application of a Gibbs-energy minimization routine for the calculation of complex chemical equilibria will be presented. Early stages of development comprise SOLGAS (1971), SOLGASMIX (1975) and ChemSage (1990). A crucial step was taken in the year of 2001, when FactSage was introduced as the fusion of ChemSage and the F*A*C*T thermochemical package developed in Montreal. The FactSage features which have recently involved the author concern mainly algorithms for the calculation of various types of phase diagrams using the Zero-Phase-Fraction method. Examples which will be demonstrated in this presentation include first-liquid projections and phase diagram sections for aqueous systems, which both represent full equilibrium states. In the para-equilibrium diagrams it is assumed that only the rapidly diffusing elements have reached equilibrium. For the Scheil constituent diagrams it is assumed that solid phases, once precipitated during cooling remain unchanged.